The ergodic properties of non-homogeneous finite Markov chains

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Abstract
The paper deals with the behaviour of finite non-homogeneous Markov chains having regular transition matrices. Two types of ergodic behaviour are distinguished, and sufficient conditions are given for each type. Chains with commutative transition matrices are specially investigated. By means of expansions in terms of the characteristic roots several types of behaviour of chains which are not ergodic are studied.

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